Motion planning for deformable object manipulation has been a challenge for a long time in robotics due to its high computational cost. In this work, we propose to mitigate this cost by limiting the number of picking points on a deformable object within the action space and simplifying the dynamics model. We do this first by identifying a minimal geometric model that closely approximates the original model at the goal state; specifically, we implement this general approach for 1-D linear deformable objects (e.g., ropes) using a piece-wise line-fitted model, and for 2-D surface deformable objects (e.g., cloth) using a mesh-simplified model. Then a small number of key particles are extracted as the pickable points in the action space which are sufficient to represent and reach the given goal. Additionally, a simplified dynamics model is constructed based on the simplified geometric model, containing much fewer particles and thus being much faster to simulate than the original dynamics model, albeit with some loss of precision. We further refine this model iteratively by adding more details from the actually achieved final state of the original model until a satisfactory trajectory is generated. Extensive simulation experiments are conducted on a set of representative tasks for ropes and cloth, which show a significant decrease in time cost while achieving similar or better trajectory costs. Finally, we establish a closed-loop system of perception, planning, and control with a real robot for cloth folding, which validates the effectiveness of our proposed method.

Planning for deformable object manipulation has been a challenge for a long time in robotics due to its high computational cost. In this work, we propose to reduce this cost by reducing the number of pick points on a deformable object in the action space. We do this by identifying a small number of key particles that are sufficient as pick points to reach a given goal state. We find these key particles through a geometric model simplification process, which finds the minimal geometric model that still enables a good approximation of the original model at the goal state. We present an implementation of this general approach for 1-D linear deformable objects (e.g., ropes) that uses a piece-wise line fitted model, and for 2-D flat deformable objects (e.g., cloth) that uses a mesh simplified model. We conducted simulation experiments on ropes and cloths, which demonstrate the effectiveness of the proposed method. Finally, the planned paths are executed in a real-world setting for two cloth folding tasks.